Question

3. A lower proportion of males ages 25 to 44 visited the gym than the proportion of males ages 45 to 64. The table below provides the numbers by age group. Test at the 2% level of signifcance.
	25 - 44	45 - 64
Visited the gym	7	33
Did not visit the gym	9	50
a. State the Null Hypothesis
b. State the Alternative Hypothesis
c. Is this a right-tailet, left-tailed or a two-tailed test?
d. State the distribution to use for the test
e. What is the test statistic (z value)?
f. What is the p value?
g. At 95% what is my significance level (alpha):
h. Decision:
i. Reason for decision:
j. Conclusion:

Answer 1

Solution

a. State the Null Hypothesis
H0: p1 = p2 Answer 1 Where p1 are p2 are population proportion of males visiting gym in the age group 25 – 44 and 45 – 64 respectively.
b. State the Alternative Hypothesis
HA: p1 < p2 Answer 2
c. Is this a right-tailet, left-tailed or a two-tailed test?
left-tailed since alternative is less than type Answer 3
d. State the distribution to use for the test
Standard Normal Distribution, i.e., N(0, 1) Answer 4
e. What is the test statistic (z value)?
Z = (p1hat – p2hat)/√[phat(1 - phat){(1/n1) + (1/n2)}] = - 0.2979 Answer 5 where p1hat = 7/16 = 0.4376 and p2hat = 33/83 = 0.3976 are sample proportions, n1 = 16, n2 = 83 are sample sizes and phat = {(n1 x p1hat) + (n2 x p2hat)}/(n1 + n2) = 40/99 = 0.4040
f. What is the p value?
p-value = P(Z < - 0.2979) = 0.3829 Answer 6
g. At 95% what is my significance level (alpha):
Significance level (alpha) = 0.05 Answer 7
h. Decision:
Accept H0 Answer 8
i. Reason for decision:
p-value > Significance level (alpha)   Answer 9
j. Conclusion:
There is not sufficient evidence to suggest that proportion of 25-44 years olds visiting gym is less than the proportion of 45-64 years olds visiting gym.    Answer 10

DONE